• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14

# Investigation into the relationship between acceleration and the angle of free fall downhill

Extracts from this document...

Introduction

Investigation into the relationship between acceleration and the angle of free fall downhill

Introduction

This is an investigation into the free fall of an object (in this case a small cart/trolley). When an object is placed on an inclined plane, the object is most likely to fall through the plane. Moreover, when the height of the plane is increased it was found that the object took less time to get to the other end. I decided to investigate the relationship between the angle of the slope of the plane and the acceleration of the object.

Aim

To investigate the extent of which the angle of the slope of the inclined plane is related to the acceleration of the object as it goes through the plane.

Independent Variables

Angle of the slope of the wooden ramp

Dependent Variables

Acceleration of the object

Controlled Variables

• Length of the plane
• Height of the plane
• Initial velocity of the object (= 0 ms-1)
• Distance travelled by the object

Hypothesis

The sine of the angle of the slope will be directly proportional to the acceleration of the object.

From

Where a is acceleration, θ is the angle of the slope, v is the final velocity, u is the initial velocity and t is time. For the second formula g is acceleration due to gravity (≈9.81 m s-2).

Equipment

• Wooden Ramp
• 1 Meter Ruler
• Stopwatch
• Bricks
• Books
• Dynamics Cart

Method of Data Collection

Procedure

1. A brick was set under one of the wooden ramp’s ends, leaving the other end touching the ground. The length (adjacent side to the angle)

Middle

0.176

0.646

0.638

0.689

0.661

0.632

0.653

0.029

The Table below shows the time taken for the cart to go downhill from the 5 experimental trials done for 5 different heights.

The uncertainty in the length and height of the plane was taken to be the half of the smallest non-zero unit on the ruler used for measurement. As a result, the uncertainty in the length and height of the plane is ±0.0005m.

It is to be noted that the time recorded used up to three decimal places, due to the use of a Casio stopwatch which differs from the usual stopwatch that would be used that would only have 2 decimal places.

The average time taken for the cart to go downhill for one of the heights was calculated from the raw data with the following mathematical formula:

The denominator was 5 because that was the number of trials experimented for one height. The average time was rounded up to 3 decimal places because the previous data had all been recorded with 3 decimal places.

The uncertainty in the average times is calculated by dividing the range of the data by 2, as shown in the following formula:

For example, for the uncertainty of the average time taken by the cart to go downhill with a height of 0.084 m:

The average time vs height was expressed in the following graph:

Processed Data

After obtaining results for the time taken for the cart to go down the slope, further calculations could be made, which include:

• Angle of inclination when the cart goes downhill
• Average Velocity of the cart, therefore acceleration of the cart too

To calculate the angle of the slope trigonometric functions were used, specifically the sine identity. The following formula was used

Therefore the angle is determined by

For example the sine and angle for the first height (0.084 m) would be as following

This calculation was applied to all the different height s and the results were expressed in the following graph, using 3 decimal places for all results:

 Height (± 0.0005 m) Distance travelled (± 0.0005 m) Sin θ(± 0.68%) Angle of slope θ (°)(± 0.68%) 0.084 0.603 0.139 8.01 0.118 0.608 0.194 11.20 0.134 0.613 0.219 12.62 0.152 0.617 0.246 14.26 0.176 0.623 0.283 16.41

The velocity was calculated taking into account the distance travelled and the time taken for the cart to go down the wooden ramp. Mathematically:

With this formula, we use as an example the set of trials for height number 1 (0.084 m):

The same calculation was done for the other heights; results were recorded and put into a table:

 Distance travelled (m)(± 0.0005) Average time (s)(± 0.001) Average Velocity (m s⁻¹)(± 0.002) 0.603 1.039 0.580 0.608 0.866 0.702 0.613 0.795 0.771 0.617 0.712 0.867 0.623 0.653 0.954

Conclusion

Improving the investigation

Measuring the heights, lengths and distances for this experiment seem to work fine, therefore they didn’t need much improvement. The main thing to improve for this experiment is the measurement of time.

The best way to eliminate the systematic error for time measuring would be to use better technology instead of just a stopwatch. This means that instead of a stopwatch, photo gates could’ve been used. Using photo gates would be better as it measures the exact point where the cart starts and finish and it can give you the value for velocity and acceleration immediately. However, the initial velocity should still be controlled carefully as the photo gate cannot control that.

Other than that, maybe a greater amount of trials could’ve been made or maybe the use of a third person with another stopwatch could help too. There are also some external factors that could’ve affected the results, for example the friction force of the ramp, maybe at times it could’ve affected the time the cart took to go downhill. This force, however, doesn’t have a major impact on the results, but for a future experiment it should be negligible in order to obtain more accurate results.

The final improvement would be to use a longer distance, using more than half a meter approximately for this experiment resulted in small results for the time. For a future experiment, using a longer distance (of at least twice as the once used for this experiment), would give a wider range of data and it would be helpful for further analysis and processing of data.

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related International Baccalaureate Physics essays

1. ## Aim: ...

- u� cosine ?) In our experiment, the angle (?) will range from 0-90 degrees, and by looking at the formula above I have predicted that as the ? increases, so should a (acceleration) (Note: the above method was found in textbook "Physics Level 9, E.K.

2. ## Investigate the Size of Craters in Sand Due to Dropped Object.

Thus, in order to sketch the graph of the volume of craters against height of dropped slotted mass, we can represent the y-axis or volume of craters by using the depth of craters itself. Calculation of the Graph: In order to sketch the graph, we need to find the average or mean of first, second, third and fourth reading.

1. ## Motion of the trolley on the inclined plane

All measurements were rounded to second decimal place. The next step to measure the acceleration was constructing the graph showing the distance dependence on time (Graph 1). The best-fit line was drawn, so were the line of maximal slope and the line of minimal slope. Then, the Graph 2 showing the average acceleration dependence on time was constructed.

2. ## Determining acceleration of free fall by of a simple pendulum.

Raw data Raw data measure Pendulum length (L/m). Uncertainty � 0.0005 m Time for 10 oscillations (T/s) Uncertainty � 0.001s Time for 1 oscillations (T/s) Uncertainty � 0.001s T2 (T/s) Uncertainty � 0.002s 1 0.95 19.72 1.972 3.89 2 0.90 19.22 1.922 3.69 3 0.85 18.78 1.878 3.53 4 0.80

1. ## The Affect of Mass on the Time It Takes an Object To Fall

it takes to hit the ground because the variable x is to a negative power close to -0.5. Furthermore, the relationship shown on the graph is not a perfect inverse square root relationship because the exponent is not exactly -0.5.

2. ## Suspension Bridges. this extended essay is an investigation to study the variation in tension ...

Experimental Procedure Apparatus Utilized and their Specifications 1. Plywood Board of dimensions 1.5 m x 1 m 2. 18 nails (9 nails hammered vertically on either side at a vertical distance of 10 cm from each other and perpendicular horizontal distance of 138 cm)

1. ## Light Intensity Investigation

picked up by the sensor- more than what is being emitted by the light bulb. * The same strength of light being emitted from the light bulb (12 volts). To control this variable we will ensure that the tuner on the ray box is at the 12-volt (the highest)

2. ## HL Physics Revision Notes

Absolute zero and the Kelvin scale: Absolute zero is 0 on the Kelvin scale and -273 on the Celsius scale. It is characterized by the complete absence of heat ? the point at which all atomic and molecular energy ceases.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to